Data Science Statistics

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# Data Science Statistics
### John Tipton
### 11/19/2021

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# Data Science Statistics 2021

Welcome:

- A little about me

- How did I get into statistics?

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# What is data science?

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# What is data science?

- Data

- Statistics

- Computation

- Interpretation/communication

- Domain knowledge

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# What is my experience in data science

- Collaborative

- Learn and work with different groups
  
  - Requires knowledge and expertise

- Dynamic

- Always new things to learn
  
  - New skills and techniques

- Communication and interpersonal skills

- Lots of writing and communication    
  
  - Networking to develop opportunities and projects
  
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# Statistics

- The mathematics underlying data science

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# Modeling

In general, all statistical models (AI/ML/etc. -- choose your favorite term) are some flavor of **regression!**

$$
y_i = \beta_0 + \beta_1 x_i + \epsilon_i
$$

```r
n <- 500
beta_0 <- 2
beta_1 <- 3
x <- seq(-1, 1, length = n)
epsilon <- rnorm(n, 0, 0.25)
y <- beta_0 + beta_1 * x + epsilon
```

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# Modeling

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# Modeling

.center[
![Regression](data:image/png;base64,#./images/regression-animation.gif)
]

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# Modeling

* If all we have is a linear model, all we can fit are linear functions

* Is this a good model fit?

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# Modeling

* How do we make that model better?

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# Modeling

* Quadratic term?

$$
y_i = \beta_0 + \beta_1 x_i + \beta_2 x_i^2 + \epsilon_i
$$

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# Modeling

* In general, statistical modeling can be written as

$$
y_i = f(x_i) + \epsilon_i
$$

.pull-left[
* Goal: find the function `$f(\cdot)$` that best approximates the observed data `$y_i$` given inputs `$x_i$`

* Example: let `$x_i$` be an image, `$y_i$` is the label cat, `$f(\cdot) = ???$`
]

.pull-right[
![](data:image/png;base64,#./images/cat-tut.png)
]

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# Modeling

* The goal is to model `$f(\cdot)$`

* What ways can we improve the model `$f(\cdot)?$`

* Break up `$f(\cdot)$` into small pieces

* Called a "basis" for `$f(\cdot)$`

* 1 and `$x$` are a basis for linear functions
    
    * 1, `$x$`, and `$x^2$` are a basis for quadratic functions

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# Modeling

* Is this basis of step functions a better fit?

.pull-left[
![](data:image/png;base64,#index_files/figure-html/unnamed-chunk-9-1.png)
]

.pull-right[
![](data:image/png;base64,#index_files/figure-html/unnamed-chunk-10-1.png)
]

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# Modeling

* What about this basis of "smooth" functions

.pull-left[

![](data:image/png;base64,#index_files/figure-html/unnamed-chunk-11-1.png)
]

.pull-right[
![](data:image/png;base64,#index_files/figure-html/unnamed-chunk-12-1.png)
]

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# What makes the DSST track unique

- Focus on the underlying mathematics that makes data science work

- Fundamental understanding of the modeling methods and techniques of statistical data science

- The strong mathematical background will enable you to learn and progress much faster to future changes in the field

- Flexibility to work in multiple domains of interest

- John Tukey -- "The best thing about being a statistician, is that you get to play in everyone's backyard."

- About 3/4 of data scientists have a [Master's degree or higher](https://ischoolonline.berkeley.edu/blog/data-scientist-salary/)

- The mathematical rigor of the DSST track make pursuing a Master's degree more approachable

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# DSST Core courses

- Introduction to Mathematical statistics
--

- Use limits to understand central limit theorem
  
  - Understand concepts like sufficiency, unbiasedness, estimation, and decision
  
--

- Experimental design
--

- Modeling designed experiments (A/B testing)
    
    - Useful for advertising/marketing
    
--

- Statistical Forecasting and Prediction
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- Modeling data over time
  
  - Accounting for autocorrelation and correlated data
  
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- Analysis of categorical data

- Generalized linear models (non-Gaussian data)

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# DSST Course Electives

- Bayesian Methods
--

- Model building, regularization, classification, and prediction
  
  - Understand constructive/probabilistic model building using probability distributions
  
--

- Nonparametric statistical methods
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- Models for data where the distribution is not Gaussian
  
  
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# Why statistics

- Statistics is the process of making decisions under uncertainty
--

- In the real world, there is **always** uncertainty
  
--

- Statistics teaches about the process and pitfalls when collecting data
--

- Is a sample of a single randomly chosen individual in the US representative?
  
--

- Statistics is the *lingua franca* of science
--

- Science and decision making is primarly concerned with statistics

* Statistics develops critical thinking and analytic skills

* Statisticians are highly paid and have rewarding careers
--

* [Statistics](https://money.usnews.com/careers/best-jobs/rankings/the-100-best-jobs?name=Statistician)
  * [Data science](https://money.usnews.com/careers/best-jobs/rankings/the-100-best-jobs?name=Data%20Scientist)

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# Why statistics

Abraham Wald

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# Why statistics

* In the UK, 70% of the covid deaths are among those that are vaccinated [Public Health England](https://www.factcheck.org/2021/11/scicheck-why-its-easy-to-misinterpret-numbers-of-deaths-among-the-vaccinated/)
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* Does the covid-19 vaccination work?

* Unvaccinated individuals are 13 times more likely to become infected and 20 times more likely to experience death due to covid-19 than vaccinated individuals [Texas Department of Health](https://www.dshs.texas.gov/immunize/covid19/data/cases-and-deaths-by-vaccination-status-11082021.pdf)
--

* Does the covid-19 vaccination work?
  
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* How can both of these be true?

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# Why statistics

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# Why statistics

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# Questions?